DS and I usually show up closer to 10 in the mornings. If you arrive later in the afternoon you should have no problem. Based on our usual morning arrival ...
MK - you have to be really early to be in the first section, so that puts you a bit further away. It is a pretty good walk from there to security. And that much farther at end of day. It might be worth getting there early.
EPCOT - Depending on timing you might miss out on Handicapped and they send you to Preferred or farther back. We try to go in Handicapped to seek a spot but, snooze you lose there. It helps if the Security by that lot is open, saves some walking.
DHS - New Handicapped lot is bigger but it still fills fast. Then you get bumped back to overflow and not a terrible walk but you have to take care as now you deal with the trams of exit traffic.
AK - Is the most successful for parking arriving later. We usually find a spot.